Densitometers are generally known in the art and are used to measure a density of a fluid. The fluid may comprise a liquid, a gas, a liquid with suspended particulates and/or entrained gas, or combinations thereof.
Vibrating densitometers can comprise a vibrating member, such as a cylinder that is exposed to a fluid under test. One example of a vibrating densitometer comprises a cylindrical conduit that is cantilever-mounted, with an inlet end coupled to an existing pipeline or other structure and with the outlet end free to vibrate. The conduit can be vibrated and a resonant frequency can be measured. As is generally known in the art, the density of the fluid under test can be determined by measuring a resonant frequency of the conduit in the presence of a fluid. According to well-known principles, the resonant frequency of the conduit will vary inversely with the density of the fluid that is contacting the conduit.
FIG. 1 shows a prior art vibrating cylinder of a vibrating gas densitometer. The prior art round vibrating cylinder may be vibrated at or near to a natural (i.e., resonant) frequency. By measuring a resonant frequency of the cylinder in a presence of a gas, the density of the gas can be determined. The prior art vibrating cylinder may be formed of metal and is constructed of a uniform thickness so that variations and/or imperfections in the cylinder wall do not affect the resonant frequency of the vibrating cylinder.
In theory, a cylinder having a perfectly round and uniform cross-sectional shape will result in only one three-lobed frequency mode shape, as is illustrated by FIG. 2. However, turning to FIG. 3, real world asymmetries caused by tolerance differences and other irregularities or imperfections will result in a supposedly circular tube, producing two vibration mode shapes that are very close together in frequency. This is problematic, as it may be practically impossible to distinguish between the two vibration modes. As a result, prior art vibrating densitometers may generate a resonant frequency value that is a mixture or combination of the two vibration modes, introducing errors into the density measurement.
FIG. 4 illustrates a prior art densitometer. The prior art densitometer includes a cylindrical vibrating member located at least partially within a housing. The housing or the vibrating member may include flanges or other members for operatively coupling the densitometer to a pipeline or similar fluid delivering device in a fluid-tight manner. In the example shown, the vibrating member is cantilever-mounted to the housing at an inlet end, leaving the opposite end free to vibrate. The vibrating member includes a plurality of fluid apertures that allow fluid to enter the densitometer and flow between the housing and the vibrating member. Therefore, the fluid contacts the inside as well as the outside surfaces of the vibrating member. This is particularly helpful when the fluid under test comprises a gas, as a greater surface area is exposed to the gas. In other examples, apertures may be provided in the housing and the vibrating member apertures may not be required.
A driver and a vibration sensor are positioned within the cylinder. The driver receives a drive signal from a meter electronics and vibrates the vibrating member at or near a resonant frequency. The vibration sensor detects the vibration of the vibrating member and sends the vibration information to the meter electronics for processing. The meter electronics determines the resonant frequency of the vibrating member and generates a density measurement from the measured resonant frequency.
To obtain accurate density measurements, the resonant frequency must be very stable. One prior art approach to achieve the desired stability is to vibrate the vibrating member in a radial vibration mode. In a radial vibration mode, the longitudinal axis of the vibrating member remains essentially stationary while at least a part of the vibrating member's wall translates and/or rotates away from its rest position. Radial vibration modes are preferred in straight conduit densitometers because radial vibration modes are self-balancing and thus, the mounting characteristics of the vibrating member are not as critical compared to some other vibration modes. FIG. 3 shows the motion of a wall of a vibrating member, exhibiting a first radial vibration mode and a second radial vibration mode. This is an example of a radial vibration mode that comprises a three-lobed radial vibration shape.
A key design criterion for a gas density cylinder is the separation the vibration mode shapes so that the mode shapes can be easily and accurately discriminated. If the vibrating member has a perfectly round cross-sectional shape and has a perfectly uniform wall thickness, there is only one three-lobed radial vibration mode. However, due to design tolerances, this is usually not achievable. Consequently, when a manufacturer attempts to make a perfectly round vibrating member with a perfectly uniform wall thickness, small imperfections result in two three-lobed radial vibrations that vibrate at two vibration modes that are very close to one another in frequency. The frequency separation between the two modes is typically very small and may be less than one Hertz, for example. With the two frequencies close together, a density determination may be difficult or impossible.
In some prior art densitometers, this problem is addressed by tuning the vibrating member so that it possesses a minimum frequency separation between the radial vibration modes. The tuning can be accomplished according to a variety of techniques, including forming lengthwise thicker and thinner regions in the vibrating member's wall in axially aligned strips. However, this prior art thickness tuning still requires extremely tight tolerances and results in manufacturing difficulties and high costs.
Therefore, there exists a need for a vibrating densitometer with increased vibration mode separation.